Halftoning via direct binary search using analytical and stochastic printer models

Structure-Aware Halftoning Using the Iterative Method Controlling the Dot Placement

Abstract Many image reproduction devices, such as printers, are limited to only a few numbers of printing inks. Halftoning, which is the process to convert a continuous-tone image into a binary one, is, therefore, an essential part of printing. An iterative halftoning method, called Iterative Halftoning Method Controlling the Dot Placement (IMCDP), which has already been studied by research scholars, generally results in halftones of good quality. In this paper, we propose a structure-based alternative to this algorithm that improves the halftone image quality in terms of sharpness, structural similarity, and tone preservation. By employing appropriate symmetrical and non-symmetrical Gaussian filters inside the proposed halftoning method, it is possible to adaptively change the degree of sharpening in different parts of the continuous-tone image. This is done by identifying a dominant line in the neighborhood of each pixel in the original image, utilizing the Hough Transform, and aligning the dots along the dominant line. The objective and subjective quality assessments verify that the proposed structure-based method not only results in sharper halftones, giving more three-dimensional impression, but also improves the structural similarity and tone preservation. The adaptive nature of the proposed halftoning method makes it an appropriate algorithm to be further developed to a 3D halftoning method, which could be adapted to different parts of a 3D object by exploiting both the structure of the images being mapped and the 3D geometrical structure of the underlying printed surface.

New Design for Compact Color Screen Sets for High-End Digital Color Press

Digital halftoning is an essential part of the process for printing color, continuous-tone content. Traditionally, the highest quality has been achieved with analog, offset lithographic presses, using color screen sets that yield periodic, clustereddot halftone patterns. Increasingly, these systems are being supplanted by digital presses that are based on either electrophotographic or inkjet marking processes. Due to the inherent instability of the electrophotographic marking process, periodic, clustered-dot halftone patterns are also widely used with such presses. However, digital presses have much lower resolution than their analog counterparts. Simply mimicking the traditional screen designs used with commercial, offset presses will result in halftone patterns that are more susceptible to moire due to the interaction between the periodic patterns used to render the different color channels. This causes instability in the printed colors. The moire can be reduced by increasing the frequency of the halftone patterns. But this may make the print appear grainier than its analog counterpart. In this paper, we introduce a principled design procedure that allows one to design color screen sets that generate periodic, clustered-dot halftone patterns that improve color stability without increasing graininess. We present experimental results to support the benefits of our new color screen set design framework.

Spatiotemporal blue noise coded aperture design for multi-shot compressive spectral imaging

Multi-shot coded aperture snapshot spectral imaging (CASSI) systems capture the spectral information of a scene using a small set of coded focal plane array (FPA) compressive measurements. Compressed sensing (CS) reconstruction algorithms are then used to reconstruct the underlying spectral 3D data cube from an underdetermined system of linear equations. Multiple snapshots result in a less ill-posed inverse problem and improved reconstructions. The only varying components in CASSI are the coded apertures, whose structure is crucial inasmuch as they determine the minimum number of FPA measurements needed for correct image reconstruction and the corresponding attainable quality. Traditionally, the spatial structures of the coded aperture entries are selected at random, leading to suboptimal reconstruction solutions. This work presents an optimal structure design of a set of coded apertures by optimizing the concentration of measure of the multi-shot CASSI sensing matrix and its incoherence with respect to the sparse representation basis. First, the CASSI matrix system representation in terms of the ensemble of random projections is established. Then, the restricted isometry property (RIP) of the CASSI projections is determined as a function of the coded aperture entries. The optimal coded aperture structures are designed under the criterion of satisfying the RIP with high probability, coined spatiotemporal blue noise (BN) coded apertures. Furthermore, an algorithm that implements the BN ensembles is presented. Extensive simulations and a testbed implementation are developed to illustrate the improvements of the BN coded apertures over the traditionally used coded aperture structures, in terms of spectral image reconstruction PSNR and SSIM.

Theoretical Bounds of Direct Binary Search Halftoning

Direct binary search (DBS) produces the images of the best quality among half-toning algorithms. The reason is that it minimizes the total squared perceived error instead of using heuristic approaches. The search for the optimal solution involves two operations: (1) toggle and (2) swap. Both operations try to find the binary states for each pixel to minimize the total squared perceived error. This error energy minimization leads to a conjecture that the absolute value of the filtered error after DBS converges is bounded by half of the peak value of the autocorrelation filter. However, a proof of the bound's existence has not yet been found. In this paper, we present a proof that shows the bound existed as conjectured under the condition that at least one swap occurs after toggle converges. The theoretical analysis also indicates that a swap with a pixel further away from the center of the autocorrelation filter results in a tighter bound. Therefore, we propose a new DBS algorithm which considers toggle and swap separately, and the swap operations are considered in the order from the edge to the center of the filter. Experimental results show that the new algorithm is more efficient than the previous algorithm and can produce half-toned images of the same quality as the previous algorithm.

A novel classification method of halftone image via statistics matrices

Existing classification methods tend not to work well on various error diffusion patterns. Thus a novel classification method for halftone image via statistics matrices is proposed. The statistics matrix descriptor of halftone image is constructed according to the characteristic of error diffusion filters. On this basis, an extraction algorithm is developed based on halftone image patches. The feature modeling is formulated as an optimization problem and then a gradient descent method is used to seek optimum class feature matrices by minimizing the total square error. A maximum likelihood method is proposed according to priori knowledge of training samples. In experiments, the performance evaluation method is provided and comparisons of performance between our method and seven similar methods are made. Then, the influence of parameters, performance under various attacks, computational time complexity and the limitations are discussed. From our experimental study, it is observed that our method has lower classification error rate when compared with other similar methods. In addition, it is robust against usual attacks.

Inverse halftoning based on the bayesian theorem

This study proposes a method which can generate high quality inverse halftone images from halftone images. This method can be employed prior to any signal processing over a halftone image or the inverse halftoning used in JBIG2. The proposed method utilizes the least-mean-square (LMS) algorithm to establish a relationship between the current processing position and its corresponding neighboring positions in each type of halftone image, including direct binary search, error diffusion, dot diffusion, and ordered dithering. After which, a referenced region called a support region (SR) is used to extract features. The SR can be obtained by relabeling the LMS-trained filters with the order of importance. Moreover, the probability of black pixel occurrence is considered as a feature in this work. According to this feature, the probabilities of all possible grayscale values at the current processing position can be obtained by the Bayesian theorem. Consequently, the final output at this position is the grayscale value with the highest probability. Experimental results show that the proposed method offers better visual quality than that of Mese-Vaidyanathan's and Chang et al's methods in terms of human-visual peak signal-to-noise ratio (HPSNR). In addition, the memory consumption is also superior to Mese-Vaidyanathan's method.

Improved dot diffusion by diffused matrix and class matrix co-optimization

Dot diffusion is an efficient approach which utilizes concepts of block-wise and parallel-oriented processing to generate halftones. However, the block-wise nature of processing reduces image quality much more significantly as compared to error diffusion. In this work, four types of filters with various sizes are employed in co-optimization procedures with class matrices of size 8 n 8 and 16 x 16 to improve the image quality. The optimal diffused weighting and area are determined through simulations. Many well-known halftoning methods, some of which includes direct binary search (DBS), error diffusion, ordered dithering, and prior dot diffusion methods, are also included for comparisons. Experimental results show that the proposed dot diffusion achieved quality close to some forms of error diffusion, and additionally, superior to the well-known Jarvis and Stucki error diffusion and Mese's dot diffusion. Moreover, the inherent parallel processing advantage of dot diffusion is preserved, allowing us to reap higher executing efficiency than both DBS and error diffusion.

Model-based error diffusion for high fidelity lenticular screening

Digital halftoning is the process of converting a continuous-tone image into an arrangement of black and white dots for binary display devices such as digital ink-jet and electrophotographic printers. As printers are achieving print resolutions exceeding 1,200 dots per inch, it is becoming increasingly important for halftoning algorithms to consider the variations and interactions in the size and shape of printed dots between neighboring pixels. In the case of lenticular screening where statistically independent images are spatially multiplexed together, ignoring these variations and interactions, such as dot overlap, will result in poor lenticular image quality. To this end, we describe our use of model-based error-diffusion for the lenticular screening problem where statistical independence between component images is achieved by restricting the diffusion of error to only those pixels of the same component image where, in order to avoid instabilities, the proposed approach involves a novel error-clipping procedure.

Inkjet printer model-based halftoning

The quality of halftone prints produced by inkjet (IJ) printers can be limited by random dot-placement errors. While a large literature addresses model-based halftoning for electrophotographic printers, little work has been done on model-based halftoning for IJ printers. In this paper, we propose model-based approaches to both iterative least-squares halftoning and tone-dependent error diffusion (TDED). The particular approach to iterative least-squares halftoning that we use is direct binary search (DBS). For DBS, we use a stochastic model for the equivalent gray-scale image, based on measured dot statistics of printed IJ halftone patterns. For TDED, we train the tone-dependent weights and thresholds to mimic the spectrum of halftone textures generated by model-based DBS. We do this under a metric that enforces both the correct radially averaged spectral profile and angular symmetry at each radial frequency. Experimental results generated with simulated printers and a real printer show that both IJ model-based DBS and IJ model-based TDED very effectively suppress IJ printer-induced artifacts.